class 12

Math

Calculus

Application of Integrals

Let $g(x)=cosx_{2},f(x)=x $ and $α,β(α<β)$ be the roots of equation

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The area between $x=y_{2}$and $x=4$ is divided into two equal parts by the line $x=a$, find the value of a.

Find the area bounded by the curve $y=(x−1)(x−2)(x−3)$ lying between the ordinates $x=0andx=3.$

Find the area of the smaller region bounded by the ellipse $9x_{2} +4y_{2} =1$ and the line $3x +2y =1$

Find the area of the region bounded by the curve $(y−1)_{2}=4(x+1)$ and the line $y=x−1$.

The area bounded by the y-axis, $y=cosx$and $y=s∈x$when $0≤x≤2π $is(A) $2(2−1 )$ (B) $2 −1$ (C) $2 +1$ (D) $2 $

Find the area of the region bounded by $x_{2}=16y,y=1,y=4$ and the y-axis in the first quadrant.

Area lying between the curves $y_{2}=4x$and $y=2x$is(A) $32 $ (B) $31 $ (C) $41 $ (D) $43 $

Find the area enclosed by the curve $x=3cost,y=2sint$